Bounds on the MMSE of "bad" LDPC codes at rates above capacity
We present bounds on the minimum mean square error (MMSE) of LDPC codes at rates above capacity. One potential application for MMSE estimation involves cooperative communication. A relay following a compress-and-forward (CF) strategy could first compute an estimate of the transmitted codeword, to reduce the level of noise in the retransmitted signal. Our first bound is based on an analysis of the LDPC belief-propagation decoder. A second bound relies on the relationship between the mutual information and the MMSE, which was discovered by Guo et al.. We compute our bounds for "bad" LDPC codes (requiring SNRs that are far above the Shannon limit, for reliable communications to be possible) and show that such codes substantially outperform "good" codes. This advantage of "bad" codes implies an interesting degree of freedom in the design of codes for cooperative communications. © 2008 IEEE.
